本文關(guān)鍵詞：幾類淺水波方程中孤立波及混沌分析　出處：《江蘇大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 混沌控制 mKdV方程 多重干擾 孤立波 Melnikov方法 Camassa-Holm方程

【摘要】：本學(xué)位論文主要借助非線性動力學(xué)理論研究了幾類淺水波方程孤立波解的穩(wěn)定性問題以及外界干擾下系統(tǒng)產(chǎn)生混沌現(xiàn)象的理論證明和數(shù)值分析。進(jìn)一步,通過Melnikov方法研究了受擾動力系統(tǒng)的混沌控制問題。本文首先研究了外部周期擾動對mKdV方程的孤立波的影響,通過改進(jìn)Melnikov方法,理論證明了孤立波在任意周期擾動下均能轉(zhuǎn)化為混沌狀態(tài)。進(jìn)一步研究發(fā)現(xiàn)更豐富的擾動頻率、更快的傳播速度以及更大的非線性參數(shù)需要更大的控制強(qiáng)度來抑制混沌。其次,研究了廣義Camassa-Holm方程中孤立波的存在性和穩(wěn)定性。非線性強(qiáng)度對孤立波的形狀和穩(wěn)定性有重要影響:當(dāng)非線性項(xiàng)的強(qiáng)度是奇次方時,該方程被證明有正孤立波,并且當(dāng)波速超過臨界值時孤立波是軌道穩(wěn)定的。當(dāng)非線性項(xiàng)的強(qiáng)度是偶次方時,該方程被證明同時有正孤立波和負(fù)孤立波,并且在任何波速下孤立波都是軌道穩(wěn)定的。最后,利用Menikov方法驗(yàn)證了在任意非線性強(qiáng)度下系統(tǒng)受外部周期擾動時孤立波都會轉(zhuǎn)變成混沌狀態(tài)。通過設(shè)計(jì)線性反饋控制器,混沌可以被控制到一個穩(wěn)定的狀態(tài)。
[Abstract]:This thesis is mainly through theoretical proof and numerical analysis of chaotic system under several kinds of shallow water wave equation stability of solitary wave solutions and the interference theory of nonlinear dynamics was studied. Further, through the Melnikov method to study the problem of chaos control of disturbed power system. This paper studies the external periodic perturbation of the mKdV equation, solitary the influence of wave, by using the improved Melnikov method is proved by the theory of solitary waves in arbitrary periodic perturbations can be transformed into a chaotic state. Further studies found that the disturbance frequency is more abundant, faster propagation speed and nonlinear parameters of the need for greater control of greater strength to suppress chaos. Secondly, study the existence and stability of the solitary wave generalized Camassa-Holm equation. Have important influence of shape and strength on the stability of nonlinear solitary wave: when the nonlinear term strength Is odd side, the equation is proved to have solitary waves, and when the velocity exceeds the critical value of solitary wave is stable. When the nonlinear term is the strength of second party, the equation is proved to be both positive and negative solitary wave and solitary wave, solitary wave at any wave velocities are orbit stable. Finally, using Menikov method to verify the external periodic perturbations in any nonlinear system by solitary wave intensity are converted into chaotic state. Through the design of linear feedback controller, chaos can be controlled to a steady state.

【學(xué)位授予單位】：江蘇大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.29

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本文編號：1412829